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Logarithmic convexity of Gini means  [PDF]
Feng Qi,Bai-Ni Guo
Mathematics , 2009, DOI: 10.7153/jmi-06-48
Abstract: In the paper, the monotonicity and logarithmic convexity of Gini means and related functions are investigated.
Some definite logarithmic integrals from Euler sums, and other integration results  [PDF]
Mark W. Coffey
Physics , 2010,
Abstract: We present explicit expressions for multi-fold logarithmic integrals that are equivalent to sums over polygamma functions at integer argument. Such relations find application in perturbative quantum field theory, quantum chemistry, analytic number theory, and elsewhere. The analysis includes the use of properties of a variety of special functions.
Maintaining partial sums in logarithmic time  [PDF]
Jochen Burghardt
Computer Science , 2014,
Abstract: We present a data structure that allows to maintain in logarithmic time all partial sums of elements of a linear array during incremental changes of element's values.
Resonances and $Ω$-results for Exponential Sums Related to Maass Forms for $\mathrm{SL}(n,\mathbb Z)$  [PDF]
Anne-Maria Ernvall-Hyt?nen,Jesse J??saari,Esa V. Vesalainen
Mathematics , 2014,
Abstract: We obtain resonances for short exponential sums involving Fourier coefficients of Maass forms for $\mathrm{SL}(n,\mathbb Z)$. This involves deriving asymptotics for the integrals appearing in the $\mathrm{GL}(n)$ Voronoi summation formula. As an application, we also prove an $\Omega$-result for short sums of Fourier coefficients.
Results about persymmetric matrices over F_2 and related exponential sums  [PDF]
Jorgen Cherly
Mathematics , 2008,
Abstract: In this paper we expose our main results about rank problems concerning persymmetric matrices over F_2 associated to some exponential sums.
The function $(b^x-a^x)/x$: Logarithmic convexity and applications to extended mean values  [PDF]
Feng Qi,Bai-Ni Guo
Mathematics , 2009, DOI: 10.2298/FIL1104063G
Abstract: In the present paper, we first prove the logarithmic convexity of the elementary function $\frac{b^x-a^x}x$, where $x\ne0$ and $b>a>0$. Basing on this, we then provide a simple proof for Schur-convex properties of the extended mean values, and, finally, discover some convexity related to the extended mean values.
On Logarithmic Convexity for Differences of Power Means  [cached]
Slavko Simic
Journal of Inequalities and Applications , 2008, DOI: 10.1155/2007/37359
Abstract: We proved a new and precise inequality between the differences of power means. As a consequence, an improvement of Jensen's inequality and a converse of Holder's inequality are obtained. Some applications in probability and information theory are also given.
On Logarithmic Convexity for Differences of Power Means
Simic Slavko
Journal of Inequalities and Applications , 2007,
Abstract: We proved a new and precise inequality between the differences of power means. As a consequence, an improvement of Jensen's inequality and a converse of Holder's inequality are obtained. Some applications in probability and information theory are also given.
On sums of powers of zeros of polynomials  [PDF]
Wolfdieter Lang
Mathematics , 1997,
Abstract: Due to Girard's (sometimes called Waring's) formula the sum of the $r-$th power of the zeros of every one variable polynomial of degree $N$, $P_{N}(x)$, can be given explicitly in terms of the coefficients of the monic ${\tilde P}_{N}(x)$ polynomial. This formula is closely related to a known \par \noindent $N-1$ variable generalization of Chebyshev's polynomials of the first kind, $T_{r}^{(N-1)}$. The generating function of these power sums (or moments) is known to involve the logarithmic derivative of the considered polynomial. This entails a simple formula for the Stieltjes transform of the distribution of zeros. Perron-Stieltjes inversion can be used to find this distribution, {\it e.g.} for $N\to \infty$.\par Classical orthogonal polynomials are taken as examples. The results for ordinary Chebyshev $T_{N}(x)$ and $U_{N}(x)$ polynomials are presented in detail. This will correct a statement about power sums of zeros of Chebyshev's $T-$polynomials found in the literature. For the various cases (Jacobi, Laguerre, Hermite) these moment generating functions provide solutions to certain Riccati equations.
Convergence of logarithmic means of quadratical partial sums of double Fourier series  [PDF]
Ushangi Goginava
Mathematics , 2013,
Abstract: In this paper we investigate some convergence and divergence properties of the logarithmic means of quadratical partial sums of double Fourier series of functions in the measure and in the $L$ Lebesgue norm.
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